MathDB

BMT 2021 General p25

Source:

September 27, 2023

geometry

Problem Statement

Let

\vartriangle BMT

be a triangle with

BT = 1

and height

1

. Let

O_0

be the centroid of

\vartriangle BMT

, and let

\overline{BO_0}

and

\overline{TO_0}

intersect

\overline{MT}

and

\overline{BM}

at

B_1

and

T_1

, respectively. Similarly, let

O_1

be the centroid of

\vartriangle B_1MT_1

, and in the same way, denote the centroid of

\vartriangle B_nMT_n

by

O_n

, the intersection of

\overline{BO_n}

with

\overline{MT}

by

B_{n+1}

, and the intersection of

\overline{TO_n}

with

\overline{BM}

by

T_{n+1}

. Compute the area of quadrilateral

MBO_{2021}T

.

Back to Problems View on AoPS